Oddness of Imaginary Dielectric Function

[xueshanxihua]

Dear developers,

As required by its oddness, we know that the imaginary part of dielectric function strictly vanishes at ω=0.

Indeed, that's what we get in an IP spectra calculation of Yambo.

However, I was confused that the usually used expression, as given in Eq.(1) of https://iopscience.iop.org/article/10.1 ... 48X/ab15d0, seems not to guarantee the oddness. I.e., the Eq.(1) can't ensure a strictly-zero-value at ω=0, since a finite broadening of spectrum will lead to an accumulation of intensity at ω=0.

Thus, I'd like to know if Yambo had use any technical approaches or additional constraints to ensure the imaginary dielectric function to be strictly zero at ω=0.



Thank you very much,

[Daniele Varsano]

Dear Zeyu,
in the equation, you mentioned it is reported the Time-Ordered version of the response function which is not strictly zero for w=0. This should be the default used by Yambo. Anyway, the ordering of the response function can be changed (by using the verbosity -V resp), you will have the following variable:

Code: Select all

GrFnTpXd= "r"                  # [Xd] Green`s function (T)ordered,(R)etarded,(r)senant,(a)ntiresonant [T, R, r, Ta, Ra]

For the expression to each time-ordering you can have a look to:
src/common/Lorentzian_FT.F
The Retarted ordering would provide exactly zero for w=0.
The time ordering is reported in the header of the output files e.g.:

Code: Select all

# - The Green`s function is T-ordered - 

so you can check your output what kind ordering you have in your calculation, and also repeat the calculation with the desired ordering comparing the outputs,
In order to check the parity (e.g. considering also negative energies).

Best,
Daniele